Dear fellows.
I don't undestand the difference between a few and few.
If my wife and I are MDs and we say that we have a few medical books in our house. Would that mean that we have a lot of books?
If we said we have few medical books, would that mean that we should have more?
Could any of you explain this to me?
Thanks.

"If my wife and I are MDs and we say that we have a few medical books in our house. Would that mean that we have a lot of books? "

No, it means you have more than a couple of books, but NOT a lot of books. If you "have a lot of books," you would say exactly that. Other ways to say it are: We have tons of books. We have books everywhere (at home). We have books coming out of the cracks. (The last is an idiom)... Actually, there are all sorts of ways to say it.

"If we said we have few medical books, would that mean that we should have more? "

In this context, yes!.. Because you are both doctors, you should (or at least one would expect you to) have more than a few books... The meaning is not always one of expectation, though. Example: I always take the Interstate (Interstate Highway) because there are few tolls. (This implies that there is an alternate route where there ARE a lot of tolls).

For any example that I can think of at the moment using "few" rather than "a few," the "few" is being emphasized. It becomes more important to the sentence.

'few' without 'a' gives a more negative idea. If someone says, I have few friends, they imply that they would like to have more friends.
If you say, 'I have a few friends', you simply state that you have 'some' friends, but not a lot. The use of 'a few' is more 'positive' or perhaps 'optimistic' than 'few'.